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Let's solve each division problem step by step.

### Key concept for dividing fractions:
To divide two fractions, you multiply the first fraction by the reciprocal (inverse) of the second fraction.

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### 1. \( \frac{1}{9} \div \frac{1}{9} \)

- Reciprocal of \( \frac{1}{9} \) is \( \frac{9}{1} \).
- Multiply: \( \frac{1}{9} \times \frac{9}{1} = \frac{1 \times 9}{9 \times 1} = \frac{9}{9} = 1 \).

Answer: \( 1 \)

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### 2. \( \frac{4}{8} \div \frac{5}{15} \)

- Reciprocal of \( \frac{5}{15} \) is \( \frac{15}{5} \).
- Multiply: \( \frac{4}{8} \times \frac{15}{5} = \frac{4 \times 15}{8 \times 5} = \frac{60}{40} \).
- Simplify: \( \frac{60}{40} = \frac{3}{2} \) or 1.5.

Answer: \( \frac{3}{2} \) or 1.5

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### 3. \( \frac{6}{9} \div \frac{3}{18} \)

- Reciprocal of \( \frac{3}{18} \) is \( \frac{18}{3} \).
- Multiply: \( \frac{6}{9} \times \frac{18}{3} = \frac{6 \times 18}{9 \times 3} = \frac{108}{27} \).
- Simplify: \( \frac{108}{27} = 4 \).

Answer: \( 4 \)

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### 4. \( \frac{3}{7} \div \frac{2}{5} \)

- Reciprocal of \( \frac{2}{5} \) is \( \frac{5}{2} \).
- Multiply: \( \frac{3}{7} \times \frac{5}{2} = \frac{3 \times 5}{7 \times 2} = \frac{15}{14} \).

Answer: \( \frac{15}{14} \) or approximately 1.07

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### 5. \( \frac{1}{12} \div \frac{12}{24} \)

- Reciprocal of \( \frac{12}{24} \) is \( \frac{24}{12} \).
- Multiply: \( \frac{1}{12} \times \frac{24}{12} = \frac{1 \times 24}{12 \times 12} = \frac{24}{144} \).
- Simplify: \( \frac{24}{144} = \frac{1}{6} \).

Answer: \( \frac{1}{6} \)

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### Summary of answers:
1. \( 1 \)
2. \( \frac{3}{2} \) or 1.5
3. \( 4 \)
4. \( \frac{15}{14} \)
5. \( \frac{1}{6} \)

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Would you like more details on any step?  
Here are 5 related questions to explore further:

1. How do you multiply fractions?
2. What is the reciprocal of a fraction?
3. How can you simplify fractions quickly?
4. What is the method to convert an improper fraction to a mixed number?
5. How do you solve a word problem involving fraction division?

**Tip:** Always simplify fractions where possible to keep calculations manageable!

Solve the following fraction division problems: 1/9 ÷ 1/9, 4/8 ÷ 5/15, 6/9 ÷ 3/18, 3/7 ÷ 2/5, and 1/12 ÷ 12/24.

Learn how to solve division problems involving fractions, such as 1/9 ÷ 1/9 and 4/8 ÷ 5/15, using the reciprocal method. This guide covers key mathematical concepts like fraction division and simplification for students in Grades 5-7.

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